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SMO 2020 Senior Round 1 Question 25

SMO · SMO 2020 Senior Round 1

Question 25

$40=2\times2\times2\times5$ is a positive divisor of $1440$ that is a product of $4$ prime numbers.

$48=2\times2\times2\times2\times3$ is a positive divisor of $1440$ that is a product of $5$ prime numbers.

Find the sum of all the positive divisors of $1440$ that are the products of an odd number of prime numbers.